So, classic economics doesn't quite make sense in a transport environment anyway. We can't be mumbling ridiculous things about monopolies in transport, when almost all transport routes run monopolies. In fact, the only transport routes which don't, tend to be deregulated buses and as I think everyone can agree, the deregulated bus network is a colossal mess.
The reason LO devolution has thus far worked, is that TfL entirely runs its operation as a means of moving passengers around London. Even Conservative mayor Boris Johnson was quite happy to lose money funding the Overground, because it kept London moving.
The reason they're popular is because TfL, in an attempt to get London moving, wants to tempt people off of other modes of transport, and onto the ones its just inherited. They grab ALL the low-hanging fruit as quickly as possible, in notable contrast to the DfT's approach, which is slow and measured (in part because they need to fund big projects on a frequent basis - with a totally different investment model). You'll notice how TfL re-furbished all the 315s and 317s in a matter of months (I think it was months), when Northern's spend the best part of a year and only just refurbished a single 158 (yes, I know they don't want to be associated with "old stock"). Again, quick wins, but done straight off the bat. Staffing stations, giving them a quick lick of paint, quick wins, but popular. No, they don't have a magic wand, and yes, sorting out the South Eastern and Southern metros will be difficult, but again, the first thing you'd see on takeover would be the quick wins, re-furbished trains (which the general public will still see as "new"), lick of paint on newly staffed stations, running a couple of extra trains in spare off-peak paths. Ta-da!!!
It's almost exactly what Virgin do when they take over a franchise - look how quickly the HSTs and 91s got re-painted and there's not that long until all of them will have the new interior. I certainly noticed Durham railway station's ticket office hours being about 2-3 hours later since they took over and everything's just a little cleaner. Small things, but it changes the public perception, which in a city like London, which needs to squeeze every bit of capacity it has out, will do a damned sight better than whatever GTR's doing with their Southern concession, by pushing those extra passengers onto those trains regardless of how well they actually run.